Spatial Operator Algebra (SOA) Discussion Group
A discussion group led by Abhi Jain is being organized to provide a forum for those interested in gaining a strong working knowledge of the Spatial Operator Algebra (SOA) analytical framework and its application to rigid/flex dynamics modeling, robotics analysis, and algorithm development. The focus of the discussion group will be on SOA theory and analytical methods rather than on software tools. A brief overview of SOA is included below. This page will contain information and resources for the discussion group.
Please fill out and submit the sign up form if you are interested in joining the group. Current list of participants.
Meetings
- The list of past meetings and slides and video material from the meetings are available here.
- Meetings schedule: Weekly on Mondays, 10-11:30am (PST).
Resources
Some of the resources listed here are avaiable only within the JPL network. Non-JPL persons can email schutte@jpl.nasa.gov with their IP address (google 'what's my IP address') so we can white list it to provide you access to these materials.
- This discussion group's webpage (i.e. this page) URL is https://dartslab.jpl.nasa.gov/soagroup/.
- The mailing list for this group is dartslab.soagroup@jpl.nasa.gov.
- An updated and revised version of the 2010 Robot and Multibody Dynamics: Analysis and Algorithms Springer book by Abhinandan Jain is available online at https://dartslab.jpl.nasa.gov/SOABook/.
- Online SOA publications.
- Slides and video from the SOA session at the 2019 DARTS Lab course on the DARTS/Dshell software are availabe at(look for the D session).
- Online Jupyter notebooks for the PyCraft computational workbench for SOA. Please register to create an account to access the notebooks.
- An expanded description of SOA.
- The 2020 DARTS Lab course on the SOA-based DARTS/Dshell and DSENDS EDL simulation software which will be held from Aug 31-Sep 4, 2020. See course page for details.
Feedback
Please use the following on-line links to provide feedback on the dicussion group. You can also use the mailing list to communicate with the whole group.
- Future topics: Please indicate preferences for future topics (and add new ones).
- Feedback comments: Any feedback comments regarding the dicussion group such as content, format, length etc.
- Areas of interest: Your areas of interest and/or what you hope to get out of the discussion group.
SOA Background
SOA is a methodology pioneered and developed at JPL since the '80s for the dynamics modeling and algorithm development of multibody systems including spacecraft, ground vehicles, robots, and molecular systems. SOA provides mathematical tools for exploiting and analyzing the underlying structure of rigid/flexible multibody system dynamics as well as techniques for developing fast computational algorithms. Novel results from the SOA body of work include
- analytical expressions for the mass matrix and its inverse for arbitrary size, rigid-flexible branched topolgy systems
- O(N) methods for rigid/flex forward dynamics
- O(N) methods for computing the operational space inertia
- constraint-embedding methods for minimal coordinate modeling of closed-topology systems
- analytical expressions for mass matrix sensitivities
- closed-form expressions and algorithms for the Fixman potential
- diagonalized dynamics formulations
SOA algorithms form the basis of the DARTS multibody dynamics software for rigid/flexible multibody dynamics, arbitrary system size topologies, smooth and non-smooth contact dynamics, and run-time configuration changes with fast computational performance. DARTS is currently in use by flight missions and technology projects within and external to JPL.
Contact info
Email: Abhi Jain (jain@jpl.nasa.gov, (818) 636-4794) or
Email: Aaron Schutte (schutte@jpl.nasa.gov, (818) 531-5758)